Multiplexing requires active feed-forwarding of PNR detector outcomes, which can be implemented using \(2 \times 2\)  “crossbar" switches.
These switches operate in two modes: a bar that effects the identity and a cross that effects the SWAP gate.
This operation can be realised through variable-transmissivity beam-splitters, or Mach-Zehnder interferometers with variable phase-shifters.
A binary tree of these kinds of switches is sufficient to move a successfully prepared state into the correct output port [1]}.
